Multi-Partite Entanglement Inequalities via Spin Vector Geometry

Abstract

We introduce inequalities for multi-partite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.

4 pages, 2 tables, 1 figure. A truncated version is published in Physical Review Letters, volume 95 issue 18, 180402 (October 2005)

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Cited by in corpus (12)

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• Quantitative entanglement witnesses
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Entanglement and nonlocality in multi-particle systems
• Multipartite Entanglement Criterion from Uncertainty Relations
• Bell-type inequalities for cold heteronuclear molecules
• Bipartite nonlocality with a many-body system
• Strengthened Bell Inequalities for Entanglement Verification
• Optimal entanglement witnesses in a split spin-squeezed Bose-Einstein condensate
• Multipartite nonlocality in the presence of particle-number super-selection rules